73. Set Matrix Zeroes

1.問題

• 如果行列中有元素為0, 讓整行或整列為0

2.想法

• 提問:

• function header, parameter

• test input

• 說明想法

  • 先標記0的位置, 掃描若為被標記的位置則將其row, col設為0

• 測試計算複雜度

3.程式碼

• O (m + n)解:

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        vector<bool> rowFlag(matrix.size(), false);
        vector<bool> colFlag(matrix[0].size(), false);
        for (int i = 0; i < matrix.size(); i++) {
            for (int j = 0; j < matrix[i].size(); j++) {
                if (matrix[i][j] == 0) {
                    rowFlag[i] = true;
                    colFlag[j] = true;
                    continue;
                }
            }
        }
        for (int i = 0; i < matrix.size(); i++) {
            for (int j = 0; j < matrix[i].size(); j++) {
                if (rowFlag[i] || colFlag[j]) {
                    matrix[i][j] = 0;
                }
            }
        }
    }
};

• O(1)解: 用第一行, 列記錄

class Solution {
public:
    void setZeroes(vector<vector<int>>& matrix) {
        int m = matrix.size(), n = matrix[0].size();
        bool isFirstRowZero = false, isFirstColZero = false;
        for (int i = 0; i < m; i++){
            if (matrix[i][0] == 0) {
                isFirstColZero = true;
            }
        }
        for (int i = 0; i < n; i++){
            if (matrix[0][i] == 0) {
                isFirstRowZero = true;
            }
        }
        
        for (int i = 1; i < m; i++){
            for (int j = 1; j < n; j++) {
                if (matrix[i][j] == 0) {
                    matrix[i][0] = 0;
                    matrix[0][j] = 0;
                }
            }
        }
        
        for (int i = 1; i < m; i++){
            if (matrix[i][0] == 0) {
                for (int j = 0; j < n; j++){
                    matrix[i][j] = 0;
                }
            }
        }
        
        for (int j = 1; j < n; j++){
            if (matrix[0][j] == 0) {
                for (int i = 0; i < m; i++){
                    matrix[i][j] = 0;
                }
            }
        }
        
        if (isFirstColZero) {
            for (int i = 0; i < m; i++){
                matrix[i][0] = 0;
            }
        }
        
        if (isFirstRowZero) {
            for (int i = 0; i < n; i++){
                matrix[0][i] = 0;
            }
        }
    }
};

4.Performance